An analytical thermal model for vertical ground heat exchangers in layered soil with thermal resistance

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The space–time temperature distribution near ground heat exchangers is a crucial factor in the rational design and a key consideration for the successful application of geothermal systems. The vertical ground heat exchangers were simplified as multiple finite cylindrical surface heat sources at various depths within the soil layers, and a mathematical model of heat transfer in layered soil considering the thermal resistance effect was established. The finite Hankel and Laplace transforms were utilized to obtain the Laplace-domain solutions to the temperature of each soil layer. These solutions were then numerically inverted using the Crump method to obtain time-domain solutions. The impact of thermal resistance on the temperature distribution within each soil layer near ground heat exchangers was evaluated. The results indicated that the proposed layered model considering thermal resistance can better characterize temperature variations at the soil layer interface. When considering thermal resistance between different soil layers, there was an increase in interface temperature above the soil layer due to heat accumulation, while there was a decrease in interface temperature below the soil layer due to reduced heat. There was evidence of a hopping phenomenon in the temperature distribution at the interfaces of adjacent soil layers. It was observed that the effect of thermal resistance on temperature response increased with increasing the thermal resistance, total heat exchange rate at the wall of ground heat exchangers and heat transfer times but decreased with increasing the radial distance. Moreover, a greater difference in thermal conductivity between adjacent soil layers led to a more significant influence of thermal resistance on temperature distribution.